How to pick the right problem-solving strategy to solve a problem
Problem-solving strategies are the ways/ methods that we choose to solve the problem. Solving the problem includes many steps: understanding the problem, devising a plan or a strategy, carrying out the plan, looking back, and choosing the best solution based on the time and space complexities.
Let’s review each strategy in this Answer and learn what kind of problems can be solved using it. We will also discuss a problem for each of these and explore how the strategy can be implemented in that problem.
Top-down method
The process of solving problems “top-down” or breaking down large overarching goals into smaller more achievable tasks begins with the aim or big picture. This approach is concerned with gaining a broad overview of the issue before going into deeper details.
Example
A to-do list app is built using a top-down methodology, which begins with defining the main features and high-level requirements. This is followed by a methodical breakdown of the components, interface design, development, and testing-based refinement.
Bottom-up method
In contrast to the top-down method, the bottom-up approach works with smaller tasks and works upward to solve the larger problem. This strategy is productive when the details of the given problems are well understood, and we want to build up to a wide solution.
Example
Techniques like bubble sort and insertion sort are implemented and tested as part of the bottom-up process for sorting algorithms. Afterward, these techniques merge to generate an efficient sorting solution.
Divide and conquer strategy
The divide and conquer approach refers to the process of dividing a problem into smaller subproblems, resolving each one separately, and then merging solutions in order to tackle the main issue. This method is helpful when complicated issues can be broken down into smaller, more manageable components.
Example
In binary search, the divide and conquer strategy divides the sorted array and compares the target with the middle element. The difficulty is effectively solved when the search is recursively limited to either the left or right half based on the comparison.
Stepwise refinement strategy
In this strategy, a simple task is progressively developed and improved upon by progressively adding more specifics and complexities. It is helpful when we want to start with a basic solution and improve it little by little.
Example
Stepwise refinement is used in building web applications in which we first make the basic frontend app and then add basic functionalities like connecting the database. In the end, we integrate the app with external APIs for additional data.
Induction
An inductive reasoning approach draws general conclusions by identifying patterns and supporting data from specific examples. This strategy is useful when we have observed patterns or trends and want to generalize them to solve a broader class of problems.
Example
Inductive reasoning is applied to the Fibonacci sequence by observing that each number is the sum of the two preceding ones. This observed pattern is generalized into a rule for generating Fibonacci numbers, demonstrating the power of inductive logic.
Analogy
In this strategy, we compare the present topic and a known or solved problem in the past. It is useful when we can apply solutions from one domain to a related problem in another to solve an unknown problem.
Example
When applying well-known techniques to new problems with similar characteristics, programmers use the analogy approach by comparing a given task with an already addressed problem.
Conclusion
The choice between these strategies depends on factors such as the problem’s complexity, our familiarity with the problem domain, the availability of relevant examples, and the specific requirements of the problem. Often, a combination of these strategies might be the most effective. Analyzing the problem’s characteristics and considering our strengths and knowledge can guide us in selecting the most appropriate problem-solving strategy.
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